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Literacy: Choosing the Best Null Model

  • Katharina A. ZweigEmail author
Chapter
Part of the Lecture Notes in Social Networks book series (LNSN)

Abstract

The last chapter has shown that “smallness” of a network is eventually a rather unsurprising feature that can be generated by very different network generating mechanisms—actually, smallness is hard to avoid. In that light, “largeness” as a much more surprising feature can be expected to be either functional or caused by constraints that are important to understand the evolution of a given network. This argument emphasizes that it is important to look for surprising structural features. This, however, requires to choose an appropriate null-model which is discussed in this chapter.

Keywords

Bipartite Graph Random Graph Degree Distribution Cluster Coefficient Multiple Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Artzy-Randrup Y, Stone L (2005) Generating uniformly distributed random networks. Phys Rev E 72:056708MathSciNetCrossRefGoogle Scholar
  2. 2.
    Chung F, Linyuan L (2006) Complex graphs and networks. American Mathematical Society, USACrossRefzbMATHGoogle Scholar
  3. 3.
    Cobb GW, Chen Y-P (2003) An application of Markov Chain Monte Carlo to community ecology. Am Math Monthly 110:265–288MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Colizza V, Flammini A, Serrano MA, Vespignani A (2006) Detecting rich-club ordering in complex networks. Nat Phys 2:110–115CrossRefGoogle Scholar
  5. 5.
    Diaconis P, Saloff-Coste L (1995) Random walk on contingency tables with fixed row and column sums. Technical report, Department of Mathematics, Harvard UniversityGoogle Scholar
  6. 6.
    Garlaschelli D, Loffredo MI (2004) Patterns of link reciprocity in directed networks. Phys Rev Lett 93:268701CrossRefGoogle Scholar
  7. 7.
    Geng L, Hamilton HJ (2006) Interestingness measures for data mining: a survey. ACM Comput Surv 38(3):9CrossRefGoogle Scholar
  8. 8.
    Gionis A, Mannila H, Mielikäinen T, Tsaparas P (2006) Assessing data mining results via swap randomization. In: Proceedings of the twelfth ACM SIGKDD international conference on knowledge discovery and data mining (KDD’06), 2006Google Scholar
  9. 9.
    Gionis A, Mannila H, Mielikäinen T, Tsaparas P (2007) Assessing data mining results via swap randomization. ACM Trans Knowl Discovery Data 1(3):article no 14Google Scholar
  10. 10.
    Gotelli NJ, Graves GR (1996) Null-models in ecology. SmithsonianInstitution Press, Washington and LondonGoogle Scholar
  11. 11.
    Guillaume J-L, Latapy M (2004) Bipartige graphs as models of complex networks. In: Proceedings of the 1st international workshop on combinatorial and algorithmic aspects of networks (CAAN)Google Scholar
  12. 12.
    Guillaume J-L, Latapy M (2004) Bipartite structure of all complex networks. Inf Process Lett 90(5):215–221MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Herlocker JL, Konstan JA, Borchers A, Riedl J (1999) An algorithmic framework for performing collaborative filtering. In: Proceedings of the 22nd annual international ACM SIGIR conference on Research and development in information retrieval, pp 230–237Google Scholar
  14. 14.
    Horvát Á-E (2013) Modelling and inferring connections in complex networks. PhD thesis, Heidelberg UniversityGoogle Scholar
  15. 15.
    Kleinberg J (2000) The small-world phenomenon: an algorithmic perspective. In: Proceedings of the 32nd ACM symposium on theory of computing, pp 163–170Google Scholar
  16. 16.
    Latapy M, Magnien C, Del Vecchio N (2008) Basic notions for the analysis of large two-mode networks. Soc Netw 30(1):31–48CrossRefGoogle Scholar
  17. 17.
    Leskovec J, Kleinberg J, Faloutsos C (2007) Graph evolution: densification and shrinking diameters. ACM Trans Knowl Discovery Data (TKDD) 1(1):No 2Google Scholar
  18. 18.
    Li M, Fan Y, Chen J, Gao L, Di Z, Jinshan W (2005) Weighted networks of scientific communication: the measurement and topological role of weight. Phys A 350:643–656CrossRefGoogle Scholar
  19. 19.
    Maslov S, Sneppen K (2002) Specificity and stability in topology of protein networks. Science 296:910–913Google Scholar
  20. 20.
    Newman ME (2010) Networks: an introduction. Oxford University Press, New YorkGoogle Scholar
  21. 21.
    Newman MEJ (2001) The structure of scientific collaboration networks. Proc Natl Acad Sci USA 98(2):404–409Google Scholar
  22. 22.
    Newman MEJ (2002) Random graphs as models of networks. Technical report, Working Paper 02-02-005 at the Santa Fe InstituteGoogle Scholar
  23. 23.
    Newman MEJ, Strogatz SH, Watts DJ (2001) Random graphs with arbitrary degree distributions and their applications. Phys Rev E 64:026118Google Scholar
  24. 24.
    Piatetsky-Shapiro G (1991) Knowledge discovery in databases. Discovery, analysis, and presentation of strong rules. AAAI/MIT Press, Menlo ParkGoogle Scholar
  25. 25.
    Schlauch W, Zweig K, Horvát E-Á (2015) Different flavors of randomness. Soc Netw Anal Min 5:eid:36Google Scholar
  26. 26.
    Spitz A, Gimmler A, Stoeck T, Zweig KA, Horvát E-Á (2016) Assessing low intensity relationships in complex networks. PLoS ONE 11(4):e0152536Google Scholar
  27. 27.
    Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442CrossRefGoogle Scholar
  28. 28.
    Zhou S, Mondragon RJ (2004) The rich-club phenomenon in the internet topology. IEEE Commun Lett 8:180–182CrossRefGoogle Scholar
  29. 29.
    Zweig KA (2010) How to forget the second side of the story: a new method for the one-mode projection of bipartite graphs. In: Proceedings of the 2010 international conference on advances in social networks analysis and mining ASONAM 2010, pp 200–207Google Scholar
  30. 30.
    Zweig KA (2011) Good versus optimal: why network analytic methods need more systematic evaluation. Open Comput Sci 1:137–153CrossRefGoogle Scholar
  31. 31.
    Zweig KA, Kaufmann M (2011) A systematic approach to the one-mode projection of bipartite graphs. Soc Netw Anal Min 1:187–218CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria 2016

Authors and Affiliations

  1. 1.TU Kaiserslautern, FB Computer ScienceGraph Theory and Analysis of Complex NetworksKaiserslauternGermany

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